Sr Examen
Integral de dx/(x^3-4) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------ dx | 3 | x - 4 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{3} - 4}\, dx$$
Integral(1/(x^3 - 4), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ 3 ___ ___\ / 2/3 ___ |\/ 3 x*\/ 2 *\/ 3 | | 2/3 / 2 3 ___ 2/3\ 2/3 / 2/3\ 2 *\/ 3 *atan|----- + -------------| | 1 2 *log\x + 2*\/ 2 + x*2 / 2 *log\x - 2 / \ 3 3 / | ------ dx = C - ------------------------------- + ------------------ - -------------------------------------- | 3 24 12 12 | x - 4 | /
$$\int \frac{1}{x^{3} - 4}\, dx = C + \frac{2^{\frac{2}{3}} \log{\left(x - 2^{\frac{2}{3}} \right)}}{12} - \frac{2^{\frac{2}{3}} \log{\left(x^{2} + 2^{\frac{2}{3}} x + 2 \sqrt[3]{2} \right)}}{24} - \frac{2^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12}$$
Gráfica
Respuesta
[src]
/ ___ 3 ___ ___\
2/3 ___ |\/ 3 \/ 2 *\/ 3 |
2/3 / / 2/3\\ 2/3 / 2/3 3 ___\ 2/3 / / 2/3\\ 2/3 / 3 ___\ 2 *\/ 3 *atan|----- + -----------| 2/3 ___
2 *\pi*I + log\2 // 2 *log\1 + 2 + 2*\/ 2 / 2 *\pi*I + log\-1 + 2 // 2 *log\2*\/ 2 / \ 3 3 / pi*2 *\/ 3
- ----------------------- - ---------------------------- + ---------------------------- + ----------------- - ------------------------------------ + -------------
12 24 12 24 12 72
$$- \frac{2^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{\sqrt[3]{2} \sqrt{3}}{3} \right)}}{12} - \frac{2^{\frac{2}{3}} \log{\left(1 + 2^{\frac{2}{3}} + 2 \sqrt[3]{2} \right)}}{24} + \frac{2^{\frac{2}{3}} \log{\left(2 \sqrt[3]{2} \right)}}{24} + \frac{2^{\frac{2}{3}} \sqrt{3} \pi}{72} - \frac{2^{\frac{2}{3}} \left(\log{\left(2^{\frac{2}{3}} \right)} + i \pi\right)}{12} + \frac{2^{\frac{2}{3}} \left(\log{\left(-1 + 2^{\frac{2}{3}} \right)} + i \pi\right)}{12}$$
=
=
/ ___ 3 ___ ___\
2/3 ___ |\/ 3 \/ 2 *\/ 3 |
2/3 / / 2/3\\ 2/3 / 2/3 3 ___\ 2/3 / / 2/3\\ 2/3 / 3 ___\ 2 *\/ 3 *atan|----- + -----------| 2/3 ___
2 *\pi*I + log\2 // 2 *log\1 + 2 + 2*\/ 2 / 2 *\pi*I + log\-1 + 2 // 2 *log\2*\/ 2 / \ 3 3 / pi*2 *\/ 3
- ----------------------- - ---------------------------- + ---------------------------- + ----------------- - ------------------------------------ + -------------
12 24 12 24 12 72
$$- \frac{2^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{\sqrt[3]{2} \sqrt{3}}{3} \right)}}{12} - \frac{2^{\frac{2}{3}} \log{\left(1 + 2^{\frac{2}{3}} + 2 \sqrt[3]{2} \right)}}{24} + \frac{2^{\frac{2}{3}} \log{\left(2 \sqrt[3]{2} \right)}}{24} + \frac{2^{\frac{2}{3}} \sqrt{3} \pi}{72} - \frac{2^{\frac{2}{3}} \left(\log{\left(2^{\frac{2}{3}} \right)} + i \pi\right)}{12} + \frac{2^{\frac{2}{3}} \left(\log{\left(-1 + 2^{\frac{2}{3}} \right)} + i \pi\right)}{12}$$
-2^(2/3)*(pi*i + log(2^(2/3)))/12 - 2^(2/3)*log(1 + 2^(2/3) + 2*2^(1/3))/24 + 2^(2/3)*(pi*i + log(-1 + 2^(2/3)))/12 + 2^(2/3)*log(2*2^(1/3))/24 - 2^(2/3)*sqrt(3)*atan(sqrt(3)/3 + 2^(1/3)*sqrt(3)/3)/12 + pi*2^(2/3)*sqrt(3)/72
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.